how to prove E(Σei^)=ΣE(yi^)-E(Σyihat^)

#1
this formula looks simple but i really don't know how to explain mathmatically
E(Σei^)=ΣE(yi^)-E[Σyi(hat)^]
i tried putting E(Σei^)=E[Σ(Yi-yihat)^] but then don;t know how to continue


thanks so much..
 
E

elnaz

Guest
#2
Hello
please attend to me, this formula is not true E(Σei^)=ΣE(yi^)-E(Σyihat^)
we have this formula in regression: Σei=Σ(yi-yihat)
now you want to take E(expectancy) of it , so we have:
E(Σei)=E(Σ(yi-yihat)) => E(Σei)=(ΣE(yi-yihat)) =>
E(Σei)=ΣE(yi)-E(Σyihat) E(Σei)=ΣE(yi)-ΣE(yihat)